Mathematics Grade 11 P1 Gauteng June 2019 Memo (Afrikaans)

Downloaded from hlayiso.com testpapers.co.za GAUTENG DEPARTMENT OF EDUCATION / GAUTENGSE DEPARTEMENT VAN ONDERWYS PROVINCIAL EXAMINATION / PROVINSIALE EKSAMEN JUNE / JUNIE 2019 GRADE / GRAAD 11 MATHEMATICS / WISKUNDE PAPER / VRAESTEL 1 MARKING GUIDELINE / NASIENRIGLYN 12 pages / bladsye

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11 GAUTENG DEPARTMENT OF EDUCATION / GAUTENGSE DEPARTEMENT VAN ONDERWYS PROVINCIAL EXAMINATION / PROVINSIALE EKSAMEN MATHEMATICS / WISKUNDE (Paper / Vraestel 1) MARKING GUIDELINE / NASIENRGLYN INSTRUCTIONS AND INFORMATION A – accuracy C.A. – continued accuracy NOTE:  If a candidate answered a question TWICE, mark only the first attempt.  If a candidate crossed OUT an answer and did not redo it, mark the crossed-out answer.  Consistent accurancy applies to ALL aspects of the marking guideline.  Assuming values / answers in order to solve a problem is UNACCEPTAB LE. INSTRUKSIES EN INLIGTING A – Akkuraatheid C.A – Volgehoue akkuraatheid LET WEL:  Indien ʼn kandidaat ʼn vraag TWEE keer antwoord, sien slegs die eerste poging na.  Indien die kandidaat die antwoord deurgehaal het en nie oorgedoen het nie, sien die deurgehaalde poging na.  Volgehoue akkuraatheid is op ALLE aspekte van die nasienriglyne van toepassing.  Dit is ONAANVAARBAAR om waardes / antwoorde te veronderstel om ʼn probleem op te los. 2

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11 QUESTION / VRAAG 1 MARKS / PUNTE: 25  standard form / standaardvorm (x – 7)(x + 1) = 0  correct factors / korrekte faktore x = 7 or / of x = – 1  both x answers / beide x antwoorde OR / OF OR / OF 1.1.1  standard form / standaardvorm √  substitution into corr. formula / vervanging in korrekte formule x = 7 or / of x = – 1  both x answers / ANY OTHER VALID METHOD / beide x antwoorde ENIGE ANDER GELDIGE METODE (3)  standard form / standaardvorm √ √  substitution into corr. formula / vervanging in korrekte formule 1.1.2 √  correct answers / korrekte antwoorde PENALISE INCORRECT ROUNDING OFF/ PENALISEER VERKEERDE AFRONDING ANY OTHER VALID METHOD / (4) ENIGE ANDER GELDIGE METODE √ √  squaring both sides / kwadreer albei kante 1.1.3  standard form /standaardvorm  factors / faktore ONLY applicable / SLEGS van toepassing:  choosing x = 2 / kies x=2 x=2 (4) 3

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11  correct factors / korrekte faktore + - +  correct critical values / 1.1.4 -7 korrekte kritieke waardes  correct inequalities / korrekte ongelykhede (3) = 486  factors / faktore  simplification / vereenvoudiging (27) 1.1.5  27 =  answer / antwoord OR / OF OR / OF ( 3 – 1) = 486  factorisation / faktorisering = 243  simplification / vereenvoudiging (243) = x+2 =5  simplification / vereenvoudiging (243 = ) x=3  answer / antwoord (4)  correct factors / korrekte faktore 1.2.1  both ratios correct / beide verhoudings korrek (2) 4

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11  x or y corr. as subj. of equation / x en y korrek as onderwerp van vergelyking  correct y answer / korrekte y antwoord  correct x answer / korrekt x antwoord 1.2.2  correct y answer / korrekte y antwoord  correct x answer / korrekte x antwoord (5) QUESTION / VRAAG 2 MARKS / PUNTE : 17  correct substitution / 2.1.1 korrekte vervanging  answer / antwoord (2) correct factors / korrekte faktore 2.1.2 is the other root / is die ander wortel correct answer / korrekte antwoord (2) 5

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11  as subject in equation (1) / .........(2) x as onderwerp in vergelyking (1) from / van (1) subst. / vervang in (2)  substitution into equation (2) / vervanging in vergelyking (2)  standard form / 2.2 standaardvorm  factors / faktore  both y values / beide y waardes ANY OTHER VALID ALTERNATIVE METHOD /  both x values / ENIGE GELDIGE ALTERNATIEF beide x waardes (6) √ √  correct prime bases / korrekte priem grondtal √ 2.3 √  simplification / √ vereenvoudiging ( )  simplification( ) vereenvoudiging  answer / antwoord ANY OTHER VALID ALTERNATIVE METHOD / (4) ENIGE GELDIGE ALTERNATIEWE METODE  common factor / 2.4 gemene faktor  equating / gelykstel:  answer / antwoord (3) 6

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11 QUESTION / VRAAG 3 MARKS / PUNTE: 19  correct answer / 3.1.1 korrekte antwoord (2)  equating correctly / 3.1.2 korrekte gelykstelling  answer / antwoord (2) p–0; 2–p; 6–2  determining 1st difference/ bepaal 1ste verskil  equating correctly for 2nd difference / 3.2.1 korrekte gelykstelling vir 2de verskil  answer / antwoord (3)   3.2.2   (4) Min. value at / min waarde by:  min value at / min waarde 3.2.3 but and  deduction about and / afleiding oor en  no terms can be negative /  explanation / verduideliking geen terme kan negatief wees nie. (3) 7

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11  formulating Anne’s gen. term / Anne’s general term: = n(n + 1) formulering van Anne se Anne se algemene term = +n algemene term  simplification / vereenvoudiging 3.3 Jerry’s general term: = (n + 1)2 – (n + 1)  formulating Jerry’s gen. term / Jerry se algemene term = n2 + 2n + 1 – n – 1 formulering Jerry algemene term = +n  simplification / vereenvoudiging BOTH ARE CORRECT / BEIDE IS KORREK  correct conclusion / korrekte gevolgtrekking (5) QUESTION / VRAAG 4 MARKS / PUNTE: 15 y = f(0) – – 1 4.1 =1 (0 ; 1) answer / antwoord ANSWER MUST BE IN COORDINATE FORM / (1) ANTWOORD MOET IN KOÖRDINAATVORM WEES 0 = – 1 1= 4.2 x–3=–6  simplification / x=–3 vereenvoudiging (x – 3 = – 6) (–3 ; 0)  answer / antwoord NO PENALTY IF ANSWER NOT IN COORDINATE FORM / GEEN PENALISERING INDIEN ANTWOORD NIE (2) IN KOÖRDINAATVORM IS NIE x = 3  x-asymptote / x-asimptoot 4.3 y =–1  y-asymptote / y-asimptoot (2) 8

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11 y shape / vorm 4.4 1 correct x and y-intercepts / korrekte x en y afsnitte –3 0 3 x correct asymptotes / –1 korrekte asimptote (3) f 4.5 –3 x 3 correct answer / korrekte antwoord (1) y= –1 =  m=  correct substitution / korrekte vervanging m=  answer / antwoord 4.6 OR / OF OR / OF f (o) = 1 and / en m= =  correct substitution / korrekte vervanging =  answer / antwoord ANY OTHER VALID METHOD / (3) ENIGE ANDER GELIGE METODE 9

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11 y – = m( x – ) y + 1 = 1(x – 3) sub. point / verv. punt (3 ; – 1) m = 1 y=x–4 substituting point correctly / 4.7 korrekte vervanging van punt ANY OTHER VALID METHOD / answer / antwoord ENIGE ANDER GELDIGE METODE (3) QUESTION / VRAAG 5 MARKS / PUNTE: 17 x = = x = –1  x-ordinate / x-ordinaat y = –(–1)2 – 2(–1) + 3  substitute into correct equation / 5.1 = –1 + 2 + 3 vervanging in korrekte vergelyking y = 4  y-ordinate / y-ordinaat C (–1 ; 4) (3) NO PENALTY FOR ANSWER NOT IN COORDINATE FORM / GEEN PENALISERING INDIEN ANTWOORD NIE IN KOÖRDINAATVORM IS NIE – x 2 – 2x + 3 = 0 x 2 + 2x – 3 = 0 factors / faktore (x + 3)(x – 1) = 0 5.2 x + 3 = 0 or / of x –1 = 0 critical values / kritieke waardes x = – 3 or / of x = 1 A(– 3 ; 0) B (1 ; 0) answer / antwoord AB = 4 units / eenhede (3) 10

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11 A(– 3 ; 0) C( –1 ; 4) m = – = – m = 2  value of m / waarde van m 5.3 substituting either point C( – 1 ; 4) or point A(– 3 ; 0)  substitute point into correct vervang punt C(–1 ; 4) of punt A(–3;0) in equation / y– = m( x – ) vervang punt in korrekte y – 4 = 2(x + 1) sub. point / verv. punt C( – 1 ; 4) vergelyking y=2x+6  answer / antwoord (3) ANY OTHER VALID METHOD / ENIGE ANDER GELDIGE METODE CE2 = (–1)2 + (2)2 substitution / vervanging =5 CE = √ answer / antwoord OR / OF OR / OF 5.4 C (–1 ; 4) and / en E (0 ; 6) substitution in correct formula / CE = √ – vervanging in korrekte formule answer / antwoord =√ (2) x =–1  answer / antwoord 5.5.1 x =–3  answer / antwoord (2)  correct critical value / korrekte kritiese waarde 5.5.2 x 1  answer / antwoord (2) 11

Downloaded from hlayiso.com MARKING GUIDELINE / MATHEMATICS P1 / WISKUNDE V1 NASIENRGLYN GRADE 11 / GRAAD 11 y 0 x  shape / vorm  maximum turning point on the x 5.6 axis to the left of the origin. / maksimum draaipunt op die x-as links van die oorsprong (2) QUESTION / VRAAG 6 MARKS / PUNTE: 7 correct substitution / 9 = a2 korrekte vervanging 6.1 a=3 answer / antwoord (2) answer / antwoord 6.2 y = 0 (1) 6.3 y 0 answer / antwoord (1) answer / antwoord 6.4 R(0 ; 1) (1) g(x) = – answer / antwoord OR / OF OR / OF 6.5 x answer / antwoord g(x) = ( ) (1) 6.6 y 0 answer / antwoord (1) TOTAL / TOTAAL: 100 12